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Dataplot Solution to the Non-Linear Fitting Problem
Problem Setup
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An analyst has a data set consisting of (x,y) pairs. Read the
data into the computer. Plot them. Carry out a non-linear
fit for the model
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Dataplot Code
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This is demonstrated with the built-in data file CHWIRUT1.DAT
(stored in the Dataplot auxiliary directory). The following
Dataplot program
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READ CHWIRUT1.DAT Y X TITLE AUTOMATIC PLOT Y X . LET A = 0.01 LET B = 0.01 LET ALPHA = 0.1 FIT Y = EXP(-ALPHA*X)/(A+B*X) . CHARACTERS X BLANK LINES BLANK SOLID PLOT Y PRED VS X PLOT RES X NORMAL PROBABILITY PLOT RES
Plot of Raw Data
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generated the following output
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Fit Output
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LEAST SQUARES NON-LINEAR FIT SAMPLE SIZE N = 214 MODEL--Y =EXP(-ALPHA*X)/(A+B*X) REPLICATION CASE REPLICATION STANDARD DEVIATION = 0.3281762600D+01 REPLICATION DEGREES OF FREEDOM = 192 NUMBER OF DISTINCT SUBSETS = 22 ITERATION CONVERGENCE RESIDUAL * PARAMETER NUMBER MEASURE STANDARD * ESTIMATES DEVIATION * ----------------------------------*----------- 1-- 0.10000E-01 0.72640E+01 * 0.10000E+00 0.10000E-01 0.10000E-01 2-- 0.50000E-02 0.40184E+01 * 0.12438E+00 0.41130E-02 0.13518E-01 3-- 0.25000E-02 0.33689E+01 * 0.18239E+00 0.60968E-02 0.10633E-01 4-- 0.12500E-02 0.33617E+01 * 0.18967E+00 0.61251E-02 0.10549E-01 FINAL PARAMETER ESTIMATES (APPROX. ST. DEV.) T VALUE 1 ALPHA 0.190378 (0.2203E-01) 8.6 2 A 0.613290E-02 (0.3495E-03) 18. 3 B 0.105271E-01 (0.8027E-03) 13. RESIDUAL STANDARD DEVIATION = 3.3616721630 RESIDUAL DEGREES OF FREEDOM = 211 REPLICATION STANDARD DEVIATION = 3.2817625999 REPLICATION DEGREES OF FREEDOM = 192 LACK OF FIT F RATIO = 1.5474 = THE 92.6461% POINT OF THE F DISTRIBUTION WITH 19 AND 192 DEGREES OF FREEDOM COEF AND SD(COEF) WRITTEN TO FILE DPST1F.DAT
Plot of Predicted Values with Raw Data
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Run Sequence Plot of Residuals
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Normal Probability Plot of Residuals
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Date created: 06/05/2001 |